3.1 Measures of Center Objectives: By the end of this section,
I will be able to 1) Calculate the mean for a given data set. 2)
Find the median, and describe why the median is sometimes
preferable to the mean. 3) Find the mode of a data set. 4) Describe
how skewness affects these measures of center.
Slide 3
Tuitions of Area High Schools St. Andrews St. Andrews St.
Elizabeths St. Elizabeths St. Joseph's Prep, Philly St. Joseph's
Prep, Philly St. Marks St. Marks St. Thomas More St. Thomas More
Tatnall Tatnall Tower Hill Tower Hill Ursuline Ursuline Wilmington
Christian Wilmington Christian Aquinas Aquinas Archmere Archmere
Cardinal O'Hara, Phillly Cardinal O'Hara, Phillly Father Judge,
Philly Father Judge, Philly Malvern Prep, Philly Malvern Prep,
Philly Monsignor Bonner, Philly Monsignor Bonner, Philly Padua
Padua Red Lion Red Lion Salesianum Salesianum Sanford Sanford
Wilmington Friends Wilmington Friends Caravel Caravel GROUP 1 GROUP
2
Slide 4
Tuition Activity 1) Estimate the tuition of your school. Hint:
All tuitions fall between $4,000 and $50,000. 2) Write your
estimate on your slip of paper. 3) Get into the two groups and get
in order from the lowest tuition to the highest tuition.
Slide 5
Find the Median 5) Each student on the end says One 6) The next
two students say Two 7) The next two students say Three 8) Keep
going until you find the middle person, or the median tuition. 9)
Report your median tuition to the class. 10) Find the mean of your
tuitions.
Slide 6
Three Measures of Central Tendency 1) Mean (sample mean):
average of a data set 2) Median: middle number of a data set 3)
Mode (modal): most frequent data point
Slide 7
Mean (or sample mean) Symbol is Symbol is Formula to find the
mean Formula to find the mean n = total number of items n = total
number of items = Greek letter SIGMA and means SUM = Greek letter
SIGMA and means SUM
Slide 8
Mean (or sample mean) The mean is SENSITIVE to Extreme Values,
called OUTLIERS. The mean is SENSITIVE to Extreme Values, called
OUTLIERS. Why? Why? 90, 92, 91, 87, 90, 95, 96, 93, 88, 87, 46
Slide 9
Median Always put data items in ORDER FIRST! Always put data
items in ORDER FIRST! Then find the middle term of the data set
Then find the middle term of the data set If there is no exact
middle, find the average of the TWO MIDDLE TERMS. If there is no
exact middle, find the average of the TWO MIDDLE TERMS.
Slide 10
Median The median is NOT sensitive to OUTLIERS. The median is
NOT sensitive to OUTLIERS. Why? Why? 90, 92, 91, 87, 90, 95, 96,
93, 88, 87, 46 46, 87, 87, 88, 90, 90, 91, 92, 93, 95, 96
Slide 11
Mode Order data first Order data first Find the data point that
occurs the most Find the data point that occurs the most You do not
have to have a mode You do not have to have a mode You can have
more than one mode You can have more than one mode
Slide 12
Write down what you think the average tuition is for area
private high schools. Write down what you think the average tuition
is for area private high schools. Find the mean, median, and mode
of the tuitions of area high schools. Find the mean, median, and
mode of the tuitions of area high schools.tuitions
Slide 13
Skewness and Measures of Center For RIGHT-skewed distributions,
the mean > median. For RIGHT-skewed distributions, the mean >
median. For LEFT-skewed distributions, the mean < median. For
LEFT-skewed distributions, the mean < median. For SYMMETRIC
distributions, the mean = median (roughly) For SYMMETRIC
distributions, the mean = median (roughly)
Slide 14
Slide 15
Finding values on Calculator 1) Input data into STAT EDIT LIST
2) Then Quit (2 nd MODE) and go to HOME SCREEN Find the MEAN 1) 2
nd STAT MATH 3.MEAN 2) 2 nd 1 to get L1. Hit ENTER. Find the MEDIAN
1) 2 nd STAT MATH 4.MEDIAN 2) 2 nd 1 to get L1. Hit ENTER